Matrix Cartan superdomains, super Toeplitz operators, and quantization

We present a general theory of non-perturbative quantization of a class of hermitian symmetric supermanifolds. The quantization scheme is based on the notion of a super Toeplitz operator on a suitable Z_2 -graded Hilbert space of superholomorphic functions. The quantized supermanifold arises as the C^* -algebra generated by all such operators. We prove that our quantization framework reproduces the invariant super Poisson structure on the classical supermanifold as Planck's constant tends to zero.Comment: 52

Supersymmetry and Fredholm modules over quantized spaces

The purpose of this paper is to apply the framework of non- commutative differential geometry to quantum deformations of a class of Kahler manifolds. For the examples of the Cartan domains of type I and flat space, we construct Fredholm modules over the quantized manifolds using the supercharges which arise in the quantization of supersymmetric generalizations of the manifolds. We compute the explicit formula for the Chern character on generators of the Toeplitz C^* -algebra.Comment: 24

Evolution of particle-scale dynamics in an aging clay suspension

Multispeckle x-ray photon correlation spectroscopy was employed to characterize the slow dynamics of a colloidal suspension formed by highly-charged, nanometer-sized disks. At scattering wave vectors $q$ corresponding to interparticle length scales, the dynamic structure factor follows a form $f(q,t) \sim \exp[-(t/\tau)^{\beta}$], where $\beta \approx$ 1.5. The characteristic relaxation time $\tau$ increases with the sample age $t_a$ approximately as $\tau \sim t_a^{1.8}$ and decreases with $q$ approximately as $\tau \sim q^{-1}$. Such a compressed exponential decay with relaxation time that varies inversely with $q$ is consistent with recent models that describe the dynamics in disordered elastic media in terms of strain from random, local structural rearrangements. The amplitude of the measured decay in $f(q,t)$ varies with $q$ in a manner that implies caged particle motion at short times. The decrease in the range of this motion and an increase in suspension conductivity with increasing $t_a$ indicate a growth in the interparticle repulsion as the mechanism for internal stress development implied by the models.Comment: 4 pages, includes 4 postscript figures; accepted for publication in Phys Rev Let

Legendrian Distributions with Applications to Poincar\'e Series

Let $X$ be a compact Kahler manifold and $L\to X$ a quantizing holomorphic Hermitian line bundle. To immersed Lagrangian submanifolds $\Lambda$ of $X$ satisfying a Bohr-Sommerfeld condition we associate sequences $\{ |\Lambda, k\rangle \}_{k=1}^\infty$, where $\forall k$ $|\Lambda, k\rangle$ is a holomorphic section of $L^{\otimes k}$. The terms in each sequence concentrate on $\Lambda$, and a sequence itself has a symbol which is a half-form, $\sigma$, on $\Lambda$. We prove estimates, as $k\to\infty$, of the norm squares $\langle \Lambda, k|\Lambda, k\rangle$ in terms of $\int_\Lambda \sigma\overline{\sigma}$. More generally, we show that if $\Lambda_1$ and $\Lambda_2$ are two Bohr-Sommerfeld Lagrangian submanifolds intersecting cleanly, the inner products $\langle\Lambda_1, k|\Lambda_2, k\rangle$ have an asymptotic expansion as $k\to\infty$, the leading coefficient being an integral over the intersection $\Lambda_1\cap\Lambda_2$. Our construction is a quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of $X$. We prove that the Poincar\'e series on hyperbolic surfaces are a particular case, and therefore obtain estimates of their norms and inner products.Comment: 41 pages, LaTe

Semiclassical almost isometry

Let M be a complex projective manifold, and L an Hermitian ample line bundle on it. A fundamental theorem of Gang Tian, reproved and strengthened by Zelditch, implies that the Khaeler form of L can be recovered from the asymptotics of the projective embeddings associated to large tensor powers of L. More precisely, with the natural choice of metrics the projective embeddings associated to the full linear series |kL| are asymptotically symplectic, in the appropriate rescaled sense. In this article, we ask whether and how this result extends to the semiclassical setting. Specifically, we relate the Weinstein symplectic structure on a given isodrastic leaf of half-weighted Bohr-Sommerfeld Lagrangian submanifolds of M to the asymptotics of the the pull-back of the Fubini-Study form under the semiclassical projective maps constructed by Borthwick, Paul and Uribe.Comment: exposition improve

Which patients are assessed by lung cancer nurse specialists? A national lung cancer audit study of over 128,000 patients across England

Background: Lung cancer nurse specialists (LCNS) are integral to the multidisciplinary clinical team, providing personalised physical and psycho-social interventions, and care management for people with lung cancer. The National Institute of Health and Care Excellence (NICE) recommend that all patients have access to a LCNS. We conducted a national study assessing whether there is variation in access to and timing of LCNS assessment. Methods: The National Cancer Action Team’s LCNS workforce census in England was linked with patient and hospital Trust data from the English National Lung Cancer Audit. Multivariate logistic regression was used to assess features associated with LCNS assessment. Results: 128,124 lung cancer patients were seen from 2007 to 2011. LCNS assessment confirmation was ‘yes’ in 62%, ‘no’ in 6% and ‘missing’ in 32%. Where (in clinic versus ward) and when (before versus after diagnosis) patients were assessed by a LCNS also varied. Older patients with poor performance status, early cancer stage, and comorbidities were less likely to be assessed; there was no difference with sex or socioeconomic group. Patients receiving any anti-cancer treatment were more likely to be assessed. Assessment was lower in Trusts with high annual patient numbers (odds ratio = 0.58, 95% confidence interval 0.37–0.91) and where LCNS caseload > 250 (0.69, 0.41–1.16, although not statistically significant), but increased where workload was conducted mostly by band 8 nurses (2.22, 1.22–4.02). Conclusion: LCNS assessment varied by patient and Trust features, which may indicate unmet need for some patients. The current workforce needs to expand as well as retain experienced LCNSs

Geometric Quantization on the Super-Disc

In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a certain super-homogeneous space. First, we define an example of a super-homogeneous manifold: a super-disc. We show that it has a natural symplectic form, it can be used to introduce classical dynamics once a Hamiltonian is chosen. Existence of moment maps provide a Poisson realization of the underlying symmetry super-group. These are the natural operators to quantize via methods of geometric quantization, and we show that this can be done.Comment: 17 pages, Latex file. Subject: Mathematical physics, geometric quantizatio